How to Pronounce Old Norse

Reconstructing the pronunciation of Old Norse is by nature approximate. In most instances, we estimate the pronunciation from spellings in manuscripts, rhymes in poetry, and spellings on runic inscriptions. There was no standard spelling. Writers and poets often employed their personal and regional pronunciation, and sounds sometimes changed over decades and centuries. The result is that reconstructed pronunciations are somewhat of a guess, with different scholars coming up with different sounding solutions. Worse, reconstructed pronunciation by Norwegians, Russians, Germans, Americans, English, Danish, Lithuanians tend to sound like the underlying native languages of the reconstructors.

A trend in the teaching of Old Norse-Icelandic is to read the texts with Modern Icelandic pronunciation while retaining the standard Old Norse spelling. This is a workable method, since the pronunciation between Old Icelandic and Modern Icelandic is not that different. One can easily alter some vowels and spellings of words in modern Icelandic to sound more archaic if one wishes, especially when pronouncing the poetry.

But how really different are Old Norse (Old Icelandic) and Modern Icelandic? With a sense of humor and yet answering a serious question Guðvarður Már Gunnlaugsson, professor at the Icelandic Manuscript Institute (Stofnun Árnamagnússonar) has pointed out, that if a modern Icelander were to meet a Viking in downtown Reykjavík, the two would understand each other. This is because much of the grammar, basic vocabulary, and pronunciation of Old Norse comes into Modern Icelandic with few changes. A considerable advantage to employing modern pronunciation is that the learner is well on the way to mastering not just Old Icelandic, but also Modern Icelandic. It is almost as if, one gets two languages for the work of learning one.  
–from Viking Language 1 by Jesse L. Byock